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Full text of "Mathematical And Physical Papers - Iii"

[From the Philosophical Magazine, Vol. L, p. 305 (April, 1851).]
AN EXAMINATION OF THE POSSIBLE EFFECT OF THE EADIATION OF HEAT ON THE PROPAGATION OF SOUND*.
INASMUCH as Laplace's formula is a rigorous deduction from the physical hypotheses adopted, there is no way of escaping from his result but by calling in question the hypotheses themselves. Now the development of heat and cold by sudden condensation and rarefaction is not merely a hypothetical cause, the only evidence of whose existence is that it explains the phenomena, but is a well-known physical fact, proved by direct experiment. That in the case of small sudden, condensations (positive or negative) the increase of temperature is ultimately proportional, ccvteris paribus, to the condensation, will not, it is presumed, be called in question. The only way, then, of escaping from the conclusion that the velocity of sound is really increased by the cause assigned is, to suppose that the heat produced by condensation passes away so rapidly by radiation that the result is the same as though condensation and rarefaction were incapable of changing the temperature of air. The main object of the present communication is to examine the consequences of such a supposition, in order to make out whether it be tenable or not.
Let us take the case of an infinite mass of homogeneous elastic fluid, acted on by no external forces, and having throughout a uniform temperature, and consequently a uniform pressure, except
* [This examination was made in consequence of the publication in the Philosophical Magazine of some papers in which the correctness of Laplace's explanation of the excess of the observed velocity of sound over that calculated by Newton was called in question. In the reprint, a few passages which are merely controversial, and of ephemeral interest, are omitted.]